What is the general solution for 1=tan(pi/4+x) ?

The general solution for 1=tan(pi/4+x) is x=pin

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1=tan(pi/4+x)

1 = tan (\frac{π}{4} + x)

x = πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n

Solution steps

1 = tan (\frac{π}{4} + x)

Switch sides

tan (\frac{π}{4} + x) = 1

General solutions for

tan (\frac{π}{4} + x) = 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

\frac{π}{4} + x = \frac{π}{4} + πn

\frac{π}{4} + x = \frac{π}{4} + πn

Solve

\frac{π}{4} + x = \frac{π}{4} + πn : x = πn

\frac{π}{4} + x = \frac{π}{4} + πn

Subtract

\frac{π}{4}

from both sides

\frac{π}{4} + x - \frac{π}{4} = \frac{π}{4} + πn - \frac{π}{4}

Simplify

x = πn

x = πn

tan (x) = \frac{6.1}{4}

4 cos (θ) = 4 - 4 cos (θ)

sin^{2} (x) + 6 sin (x) + 5 = 0

cos (x) = \frac{1}{3}, 0 < x < \frac{π}{2}

3 + 2 sin (θ) = 3 + 2 cos (θ)

What is the general solution for 1=tan(pi/4+x) ?
The general solution for 1=tan(pi/4+x) is x=pin